Subgroups — D₂₁×C₁₁⋊D₁₁ #23779057

Order 10164.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊(C₁₁⋊D₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁²×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₁⋊D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊(C₁₁⋊D₁₁)	—	3	1	no	—
7	C₁₁²×D₇	—	3	1	no	—
8	C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic, complemented
9	D₃×C₁₁⋊D₁₁	—	7	1	no	maximal, Hall
10	D₁₁×D₂₁	—	11	12	no	maximal
11	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃⋊(C₁₁⋊D₁₁)	—	7	1	no	—
13	D₃×C₁₁²	—	7	1	no	—
14	C₃×C₁₁⋊D₁₁	D₇	1	1	yes	characteristic, complemented
15	C₂×C₁₁⋊D₁₁	—	21	1	no	Hall
16	D₂₃₁	—	11	12	no	—
17	C₁₁×D₂₁	D₁₁	1	12	yes	complemented
18	C₃×C₇×D₁₁	—	11	12	no	—
19	C₃×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₁₁	—	33	12	no	—
21	C₂×C₁₁²	—	21	1	no	—
22	C₁₁⋊D₁₁	—	21	1	no	—
23	C₁₁⋊D₁₁	D₂₁	1	1	yes	characteristic, direct product factor
24	C₃×C₇×C₁₁	C₂×D₁₁	1	12	yes	complemented
25	D₇₇	—	33	12	no	—
26	C₇×D₁₁	—	11	12	no	—
27	C₁₁×D₇	—	3	12	no	—
28	D₃×D₁₁	—	77	12	no	—
29	C₁₁²	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₂₁	—	121	1	no	Hall
31	C₇×C₁₁	D₃×D₁₁	1	12	yes	complemented
32	D₃₃	—	77	12	no	—
33	C₃×D₁₁	—	11	12	no	—
34	D₃×C₁₁	—	7	12	no	—
35	C₂×D₁₁	—	231	12	no	—
36	C₂×C₃×C₇	—	121	1	no	—
37	D₂₁	—	121	1	no	—
38	D₂₁	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
39	C₃×C₁₁	D₇×D₁₁	1	12	yes	complemented
40	C₂×D₇	—	363	1	no	Hall
41	C₂×C₁₁	—	21	12	no	—
42	D₁₁	—	11	12	no	—
43	D₁₁	—	231	12	no	—
44	C₃×C₇	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₇	—	121	1	no	—
46	D₇	—	3	1	no	—
47	D₇	—	363	1	no	—
48	C₂×D₃	—	847	1	no	Hall
49	C₁₁	D₁₁×D₂₁	1	12	yes	complemented
50	C₇	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	121	1	no	—
52	D₃	—	7	1	no	—
53	D₃	—	847	1	no	—
54	C₂²	—	2541	1	no	Sylow
55	C₃	D₇×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	21	1	no	—
57	C₂	—	121	1	no	—
58	C₂	—	2541	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₃×C₇×C₁₁²
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃⋊(C₇⋊(C₁₁⋊D₁₁))	C₂	semidirect
2. C₁₁²×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₁⋊D₁₁	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
8. C₇×C₁₁⋊D₁₁	D₃	semidirect
11. C₇×C₁₁²	C₂×D₃	semidirect
14. C₃×C₁₁⋊D₁₁	D₇	semidirect
17. C₁₁×D₂₁	D₁₁	semidirect
19. C₃×C₁₁²	C₂×D₇	semidirect
23. C₁₁⋊D₁₁	D₂₁	direct (N × H)
24. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
29. C₁₁²	C₂×D₂₁	semidirect
31. C₇×C₁₁	D₃×D₁₁	semidirect
38. D₂₁	C₁₁⋊D₁₁	direct (N × H)
39. C₃×C₁₁	D₇×D₁₁	semidirect
44. C₃×C₇	C₂×C₁₁⋊D₁₁	semidirect
49. C₁₁	D₁₁×D₂₁	semidirect
50. C₇	D₃×C₁₁⋊D₁₁	semidirect
55. C₃	D₇×C₁₁⋊D₁₁	semidirect

Subgroups — D21×C11⋊D11 #23779057

Conjugacy classes of subgroups

Complements

Subgroups — D₂₁×C₁₁⋊D₁₁ #23779057